Some new results in $ \mathcal{F} $-metric spaces with applications

Amer Hassan Albargi; Amer Hassan Albargi

doi:10.3934/math.2023528

AIMS Mathematics

2023, Volume 8, Issue 5: 10420-10434. doi: 10.3934/math.2023528

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Research article

Some new results in $ \mathcal{F} $-metric spaces with applications

Amer Hassan Albargi ^,

Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Received: 04 January 2023 Revised: 15 February 2023 Accepted: 21 February 2023 Published: 01 March 2023
MSC : 46S40, 47H10, 54H25

In this research article, we give the notion of graphic $ F $-contraction in the setting of $ \mathcal{F} $-metric space and establish some fixed point results. We also supply some examples to demonstrate the brilliance of the established results. We also establish some fixed point results for orbitally continuous and orbitally $ G $ -continuous graphic $ F $-contractions as applications of our main results. Also, we discuss the existence and the uniqueness of solutions of functional equations involving in dynamic programming.
- fixed point,
- $ \mathcal{F} $-complete metric space,
- generalized contraction,
- graphs,
- dynamic programming
Citation: Amer Hassan Albargi. Some new results in $ \mathcal{F} $-metric spaces with applications[J]. AIMS Mathematics, 2023, 8(5): 10420-10434. doi: 10.3934/math.2023528

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Abstract

In this research article, we give the notion of graphic $ F $-contraction in the setting of $ \mathcal{F} $-metric space and establish some fixed point results. We also supply some examples to demonstrate the brilliance of the established results. We also establish some fixed point results for orbitally continuous and orbitally $ G $ -continuous graphic $ F $-contractions as applications of our main results. Also, we discuss the existence and the uniqueness of solutions of functional equations involving in dynamic programming.

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